The sum of digits in a two-digit number is 14. If you double the reversed number and add the result to the original number, the sum would be 222. Find the original number.
+23246 Let the ten's digit of the original be x and the one'e digit be y.
The value of the original number is: 10x + y
The value of the reversed number is: 10y + x
If you double the reversed number and add the result to the original number, you get 222:
This equation is: 2(10y + x) + (10x + y) = 222
20y + 2x + 10x + y = 222
12x + 21y = 222
4x + 7y = 74
Since the sum of the digits of the number is 14: x + y = 14
Combining these two equations: 4x + 7y = 74 ---> 4x + 7y = 74
x + y = 14 ---> x -4 ---> -4x - 4y = -56
Adding down the columns; 3y = 18
y = 6
Since x + y = 14: x = 8
